2020: challenges for stellar evolution & formation - G. Chabrier CRAL, ENS-Lyon / U. Exeter

2020: challenges for stellar evolution & formation

                   G. Chabrier
            CRAL, ENS-Lyon / U. Exeter

I) Transport properties
Understanding energy transport in stellar/planetary
  interiors (convection, turbulence, accretion,…)

Motivation for time-implicit multi-D simulations

Stellar physics/evolution rely on various processes characterised by very different time/length scales
           Convection, pulsation, rotation, dynamo, nuclear burning, turbulence, radiation transport …

One-dimensional stellar evolution models: rely on phenomenological description of hydrodynamical
processes:

        ☛ Convection: Mixing Length Theory
             all substellar/stellar objects: a few MJup to a few 100 M¤

         ☛ Pulsation: time-dependent convection models with several free parameters (up to 7 !)
            radial/non-radial pulsators: Cepheids, RR-Lyrae, Delta Scuti, γ Doradus

         ☛ Rotation: formalism (Zahn 1992) with several free parameters
    Mixing + transport of angular momentum: Sun, solar type stars, red giants, pre-SN stages (final yields, GRB’s, hypernovae)

         ☛ Magnetic fied:

          ☛ Accretion: phenomenological description of mass/heat redistribution of accreted matter
               Very early stages of evolution: from brown dwarfs ➝ massive stars

         ☛ Pre-SN stages
one-D Phenomenological approaches have reached their limits
To match high quality data, we need sophisticated tools and models

Multi-dimensional models
       •    Anelastic approach: filter sound waves (ASH code)
            Restricted to very low Mach number flows: convection in stellar cores (M ≲ 10-2)
            not appropriate for most asteroseimological studies
       • Compressible hydrodynamical codes (FLASH, DJEHUTY, PENCIL, ZEUS, ...)
       ☛ based on explicit time integration

       du(t)
             = f (u(t))                 un+1 = un +         tf (un )       conditionally stable: ∆t < ∆tstab
        dt

                                                         x
Time step is limited: ∆t < ∆tCFL =                                Courant-Friedrich-Lewy condition
                                                    |u| + cS
   ➡       Motivation for using time-implicit methods:
       du(t)
             = f (u(t))                  un+1 = un +           tf (un+1 )        unconditionally stable
        dt
                     No stability limit on the time-step
   → Appropriate methods to describe most of stellar physics problem:
                    τevol = τtherm, τconv, τrot, τnuc >> τdyn

            adapted for problems with various stiff scales (e.g disparate timescales)
            Time step choice is driven by accuracy and physical considerations

Characteristic timescales in the envelope of a Cepheid type star
                     (radial pulsator - 5 M¤, Teff=5500K)

Hydro τCFL ~ 102 s

Early stages of accretion history

                                                                  Bayo et al. 2011
  Text                                                           λ Orionis (~5Myr)
  Spread in the HRD:
  Well know problem: spread in Teff-
  L diagram of young cluster
  members (1-10 Myr)

     Age spread?

➙Accretion at early stages of
evolution can affect the evolution                      All 1 Myr
even after a few Myr and produce the
observed HRD spread
              M
     tacc   =    ⌧ tKH
              Ṁ
  No need to invoke an age spread
(Baraffe et al.2009, 2010, 2012)

                                                             6

large (compressible) convective zones
Convection in a red giant                        Convection in a young Sun (~Myr)
  5 Msol Teff=4500 K                                    Rconv = 0.60 Rstar
   Rconv = 0.80 Rstar           CFLhydro ~ 100      large convective zone

                                                       Overshooting
                                                        J, B, Li,…

    ∆t ~ 2.104 s ~ 0.23 d
    t ~ 13 years stellar time
   Viallet et al. ’11, ‘13                           Pratt et al. in prep

Comparison vconv (MLT, 1D) vs 1/2 (2D and 3D) for a young Sun

              4.5
              4.0
  log(vrms)

              3.5
              3.0

                                                   1D
                                                   2D, 2562
                                               ●   3D, 1283
              2.5

                    5.0e+10          1.0e+11           1.5e+11        2.0e+11

                                               r(cm)             Pratt et al. in prep

convective turnover timescale (~l/Vrms) -> magnetic braking (torque) (Matt et al ’15)

II) Magnetic field
Dynamo generation, interaction convection-magnetic field

Effect of rotation

Taylor-Proudman theorem: velocity uniform along the rotation axis =>
convective motions = columnar patterns with a charactristic length scale
perpendicular to the rotation axis  Reduces the efficiency of large-scale thermal convection to transport
the internal heat flux

 Effect of magnetic field

 Effect of rotation and/or magnetic field ->
 inhibates large-scale convection => α=l/Hp < 1

☛ possible explanation for the eclipsing BD binary of Stassun et al. 2006
  (Chabrier et al. 2007)

3D HD simulations: Rotation of fully convective objects

                                                  Same, but in a more rapidly rotating simulation (10x faster)
Radial velocity Vr on a surface near the top of
a simulation of a slowly rotating M-dwarf.        The rotation has organised the convection into organised rolls.
Up flows are reddish down flows are blue-ish.     (Interior rotation profile constant on cylinders, reflects
                                                     the Taylor-Proudman constraint)

                                                                               M. Browning , in prep

3D MHD simulations
• Development of differential rotation strongly affected by magnetic fields
• Magnetic field also impact the convective flows
 weakening of the convection (along the lines of Chabrier et al. 2007)

           Quenching Differential Rotation

                                                                  Differential rotation
                                                                  established in hydro,
                                 MHD           hydro              reduced in MHD

                                                                (Browning 2008)

       At lower ME, find less quenching of differential rotation

III) Atmospheric processes in cool atmospheres
Radiation-hydrodynamics, grain formation, non-equilibrium chemistry
         (cool giants, cool dwarfs, brown dwarfs, exoplanets)

(Freytag et al. 2013)

☛ Better agreement for LMS (MKG types)
                    (Baraffe, Homeier, Allard, Chabrier, 2015, sub.)

                                                                       quadruple system LkCa
                                                                        (Torres et al. 2013)

☛ Important for the determination of the age of young clusters
☛ Important for the characterisation of planets around M-dwarfs (SPIROU, SPHERE, PLATO)

IV) Star / Brown dwarf / Planet formation
(Dominant) formation mechanisms, stellar/BD IMF, Galactic (baryonic) census

Brown dwarf mass function

                                      T                Y        Reid et al. ’04
                                                               + Cruz et al. ’07

nBD≈nMS/3≈0.03 pc-3
         ρBD≈ρMS/30≈0.001 Msolpc-3

NBD/N* = 1/4 - 1/3   WISE (now !)~1/5

                              Chabrier ASSL, 2005

Tremblin et al., in prep.

Star/Brown dwarf formation

            Can we test these ideas ?

            ALMA will offer the spatial resolution required

            Synthetic observations done with the ALMA simulator
            Included in the Gildas software

           Commerçon
           André,          etPeretto
                  Hennebelle, al. 2012
                                     2007

I) Transport properties
      Understanding energy transport in stellar/planetary
        interiors (convection, turbulence, accretion,…)

                     II) Magnetic field
  Dynamo generation, interaction convection-magnetic field

III) Atmospheric processes in cool atmospheres
Radiation-hydrodynamics, grain formation, non-equilibrium chemistry
         (cool giants, cool dwarfs, brown dwarfs, exoplanets)

       IV) Star / Brown dwarf / Planet formation
(Dominant) formation mechanisms, stellar/BD IMF, Galactic (baryonic) census

Conroy, van Dokkum et al.

  ETGs

      MW
Chabrier, Hennebelle & Charlot, 2014